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Algebra Redux

Algebra Redux

By Gene Wilburn

“On Algebra — We’re a month into it, and I’m planning to start a real protest movement, one to have X and Y removed from the alphabet. Z is also suspect as far as I’m concerned…Damn it! They put a man on the moon; can’t they find some way to end the scourge of Algebra?” ~ Huston Piner, My Life as a Myth

“I can explain to you why algebra is useful. But that is not what algebra is really for.” He moved his fingers gently on my temples. “It’s to keep what is in here healthy. PE [exercise] for the head. And the great thing is you can do it sitting down” ~ Mal Peet, Tamar

It pains me that math gets so little cred as a form of mental satisfaction. Oh, everyone respects it, in the way you respect quantum physics — good stuff, yup, the stuff of the universe, yup — just don’t get it near me! Crikey, there’s a horse that can count better than I can. I mean, are you serious? Mental satisfaction?

I don’t mean the satisfaction of the accountant whose books balanced, though there is likely a smattering of it there as well. I mean the pure pleasure of climbing the mountain of numeric relationships and reaching an understanding, and a point of view, you never thought you could. It doesn’t have to be advanced calculus. Mere algebra will do.

But first, a disclaimer. I really like algebra, though I’m aware that many of my friends would consider this a personal failing on my part. Yet when I was in grade school I deeply disliked math because I found arithmetic, such as doing long division on paper, indescribably boring. And frustrating, because I’ve never been very good at arithmetic. I’d nickel and dime myself on tests, making little arithmetic errors here and there even though I knew how to solve the problems. And I’ve never been very solid on the times tables either. Some part of my brain just doesn’t take to arithmetic, and those were the days before electronic calculators were invented. All arithmetic was done by hand.

So, what happened to make me like algebra? Two things: the math itself, and a fantastic high-school math teacher. When it’s introduced to you by an articulate, witty and cool teacher, algebra becomes almost electric.

I just got it, right off. It was ‘a’, ‘b’, ‘c’ and ‘x’, ‘y’, and ‘z’ used symbolically to store values. Just like numeric variables in a computer language (though I didn’t know about them at the time). That plus the sheer power of the equal sign (=). If you can determine equality in some mathematical relationship, you can then solve for its components.

And you can do anything to the equation and it’s still true as long as both sides get the same treatment. Factoring is just a way of simplifying the equation. And sometimes when two equations are related, you can work out the variables in common based on some tricky, but nifty logic. And then there are inequalities like “<”, “>”, “=<”, or “=>”, not to mention getting involved with “nots” and “ands”. Talk about sharpening up your logic circuits.

Of course algebra was considered an essential skill for anyone going into science or engineering. I thought, like many others in the late 50s, that I was Cape Canaveral bound as an engineer or scientist. There were two kinds of teenage boys when I was one: those who wanted to be James Dean, and those who wanted to be a younger version of Werner Von Braun. Alas, I was one of the latter. I was not one of the cool kids.

But, it was not to be. As Mae West said, “I used to be Snow White, but I drifted.” I spent a year in engineering, studying calculus among other challenging studies, but the tidal currents of my mind pulled me to the Humanities, especially literature, philosophy, and art, and I never saw advanced math again. At least not for many years.

Then I retired. Casting about for things that could challenge my brain to keep it healthy during retirement, I began doing sudoku and crossword puzzles, and although I liked them, I didn’t feel I was getting the right kind of challenge. A small tendril of memory teased my brain into thinking about math again and I began to wonder if I could get back into it. So I tried it.

My favourite book series in math and engineering is the Schaum’s Outline series. They’re terse but full of problems to be solved. They guide you through the first steps in solving equations after every new concept, then leave you on your own, only providing the correct answers. You learn a lot trying to reason out why your answer isn’t right, and feel good when you’re on target. It’s totally hands-on learning. So I started with Schaum’s Outline of College Algebra, regaining familiarity with math and undoubtedly growing a set of new neurons.

What I noticed, parenthetically, was that the more I studied algebra, the sharper my mind felt. It’s as if my brain highly welcomed a return to this side of its operations. But then, after a couple of years, for reasons I cannot remember, I drifted again, and quit studying math.

Recently I’ve begun to feel mentally sluggish, beyond just forgetting things and wondering why I’m staring at the pantry shelves. I’ve started to feel not as sharp. Then another new tendril of thought got through to me — I think tendrils may be how the subconscious communicates with the conscious mind — and I remembered how good studying math made me feel.

And so, the arithmetically clumsy me is going to return to studying algebra. Completing the square, here I come.